Calculating the Moment Area of a Triple Extension Ladder

Hi Spockdaz,

You will need to draw a cross section of the ladder and divide it up into individual rectangular plates. Determine the resultant neutral axis (NA) of these plates. Then for every plate determine Ay^2 (where A=Area and y=distance from NA) Also determine its own Inertia bd^3/12. (b=breadth d=depth) Summate all the Ay^2 and bd^3/12 This is your Inertia about your chosen axis. You then may need to repeat the exercise for a second NA at right angles to the first.

By the way, check your material. 69000MPa is impossible

Best of luck. I know it's tedious, but stick at it!

Stewie

Dear Stewie,

Thankyou for the advice I will calculate as you've suggested, once I've calculated this I will then need to calculate the Total deflection span of the ladder using simply supported both ends with point load in the middle of the three sections. The problem with this is that the ladder is extended over total length (span) but is broken down into 3 sections and they overlap eachover. Each section has different lengths (The beam is not one continouus section) Can this be achieved by the 1WL3/48EI principle or otherwise.

Your input would be greatly appreciated.

Regards

Spockdaz

Yes Spockdaz it can be achieved this way.

If the ladder is inclined, you will have to resove the W into a force at right angles to the ladder ie WCosA (where A is the angle of inclination of the Ladder.

The beam deflection is then given by D=(W*cosA*L^3)/48EI

Assume I as the mean of the three Is you have calculated

However, conservatively you would ignore Angle A and you would have your own formula again. Please note, the "L" term is cubed

BoL Stewie

spockdaz,

A diagram would be best. If the ladder is horizontal and simply supported at each end, it is a beam with three sections having moment of inertia I₁, I₂ and I₃ respectively. If you load it with a point load at midspan, the moment is PL/4 at the middle and 0 at each end, a triangular moment diagram.

If you neglect the overlap of each section, you could consider the moment diagram divided by the applicable EI and calculate deflection based on Conjugate Beam theory or other method of your choice.

If you want to consider the effect of the two overlaps, you have to break it down further and calculate the forces between ladders each end of the overlap. These forces will cause additional rotation which will increase the deflection at the center.